Solution of internal erosion equations by asymptotic expansion

• Main Authors: Dubujet P., Parron Vera M.A., Khamlichi A., Bezzazi M., Yakhlef F.
• Format: Article
• Language: English
• Published: EDP Sciences 2012-07-01
• Series: MATEC Web of Conferences
• Subjects: Porous media; internal erosion; Darcy law; consolidation; asymptotic expansion
• Online Access: http://dx.doi.org/10.1051/matecconf/20120110007

One dimensional coupled soil internal erosion and consolidation equations are considered in this work for the special case of well determined sand and clay mixtures with a small proportion of clay phase. An enhanced modelling of the effect of erosion on elastic soil behavior was introduced through damage mechanics concepts. A modified erosion law was proposed. The erosion phenomenon taking place inside the soil was shown to act like a perturbation affecting the classical soil consolidation equation. This interpretation has enabled considering an asymptotic expansion of the coupled erosion consolidation equations in terms of a perturbation parameter linked to the maximum expected internal erosion. A robust analytical solution was obtained via direct integration of equations at order zero and an adequate finite difference scheme that was applied at order one.